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Determining mean Length of Day and DeltaT formula

Using observed data for 500 BCE to 1600 CE from [Stephenson, 2004] and for 1650 CE to 1990 CE from IERS, in the below section the change in LOD and Delta T are described.

Mean Length of Day (LOD)

The following mean changes in Length of Day (LOD) are depicted in the below figure:

 Changing LOD

Interesting to see that there looks to be a periodicy of around 1440 and 1550 years (also mentioned by Stephenson ([1997], page 516), if people know such a cycle and have some proof due to an astronomical/geophysical process, let me know.
It could be this periodicy is caused by the splining methodology  used (based on the ideas of Slutzky [1937]), but I doubt that.
Another reason for a spurious periodicy could be due to the sampling of only a limited amount of eclipses (Stephenson's pool of observations), but I think that that would not results in such a long term periodicy, because:

Linking the seen periodicy with possible geophysical events

Stephenson [Stephenson, 1997, page 513] gives an possible explanation what causes the periodicy:
With regard to the quasi-periodic fluctuations on a timescale of some 1500 years, a possible mechanism would appear to be electromagnetic coupling between the core and the mantle of the Earth. This is the most likely cause of the decade fluctuations (Lambeck, 1980, p. 247).
Another possible reason he gives is the change of sea-level variations (Lamb, 1982); "as significant long-term alterations in climate have been detected in the last few milennia".

Another reason might be the Dansgaard-Oeschger (DO) warming events, (with a possible solar origin) which are events spaced by 1470 years (which is close to my determined periodicy value of 1440 and 1550 years).
The astronomical year of a DO warming event is on -9658 - 1473*event#
With: event# = an positive/negative integer

The periodicy of DeltaT seems to reach zero around 1820 CE, so that would be a DO warming event# around -7 or -8 (-7.8 to be specific).

Mean Delta T

The below mean DeltaT graph is determined using the my above change in LOD formula. The following graphs are depicted:
DeltaT

Conclusion

The parabolic formula provided by Stephenson to calculate the mean DeltaT is perhaps lacking enough elements to predict the DeltatT (or LOD) accurate enough over the whole time period of 500 BCE to say 1300 CE (differences smaller than 10%). This additional periodic term in the formula gives a better accuracy then only a parabolic formula.
If you want to test the formula (one can use Excel XLA file), let me know.

The DeltaT formula

'using Stephenson&Morrison [2004] as the basis (n.dot = -26"/cy^2):
StartYear = 1820 [year]
Average = 1.80 [msec/cy]
Periodicy = 1443 [year]
Amplitude = 3.76 [msec]
Y2D = 365.25
OffSetYear = (JDutfromDate(StartYear, 0) - JDNDays) / 365.25

DeltaTVR = (OffSetYear ^ 2 / 100 / 2 * Average + Periodicy / 2 / Pi * Amplitude * (Cos((2 * Pi * OffSetYear / Periodicy)) - 1)) * Y2D [msec]

More generally used formula (although Stephenson's table look is better [or above formula which follows the table better]):
COD is the LOD Change (normally: 1.7 [msec/cy])
DeltaT = OffSetYear ^ 2 / 100 / 2 * COD * Y2D [msec]

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Major content related changes: May 3, 2006